The result is that they are seven points off fourth place and 11 behind Chelsea. The Blues are not a flawless team, but they do have enough good players to be sure of a top-four finish, which is more than can be said of Arsenal.

Arsene Wenger's side might have recovered to take a point, but they did not deserve one. The distance between the sides was far wider in the first half than the second.

The game, in a sense, was decided before half-time. But, in another, it had been decided with every day of drift, with every diffident window that Arsenal have wasted for the last few years.

As the travelling fans made very clear, this Arsenal squad is in need of heavy investment. They robustly advised their club to spend money, and wondered aloud what exactly chief executive Ivan Gazidis does in his job.

Arsenal's famous 'self-sustaining model' can look fairly exposed at Chelsea, a club with the opposite problems. Here at Stamford Bridge, there may be too much what Arsenal lack – purpose, ambition and ruthlessness – but perhaps not enough of the patience which Arsenal seem to be drowning in.

Not everyone would hold up Chelsea as a perfectly-run club but they have won the Premier League twice, the FA Cup four times and the Champions League since Arsenal lifted anything.

Of course, winning is easier when you buy better players. That, more than anything, seemed the difference between these two flawed sides in the first half.

Olivier Giroud is an admirable centre-forward, a French champion and France international. But he is not an exceptional player, and is no replacement for Robin van Persie. At £12m, he was fairly priced.

Mata, though, is an exceptional player, of remarkable imagination and technique. He cost roughly twice what Giroud did.

Arsenal might have bought him, but they did not. And yesterday he showed them what they missed.

So soon after Pep Guardiola's snub to Roman Abramovich and the collapse against Southampton, it was an afternoon when victory of any sort would prove significant and timely for Chelsea.

Backlash

With Abramovich in attendance for the first time this year, the absence of any tangible sign of backlash against Rafael Benitez from the home fans was notable.

Arsene Wenger was clearly furious on the touchline at the way his players persistently stood off Chelsea and allowed Mata and Hazard dictate the match.

Chelsea were on the front-foot from the very first minute when they had a plausible penalty appeal waved away after Abou Diaby appeared to man-handle Oscar.

With Ramires and Lampard dominant in central midfield and Mata, Oscar and Hazard all initially inter-hanging to great effect further forward, it was a reminder of the basic differences in quality between the two teams.

That was particularly striking when Giroud missed an excellent chance to put Arsenal into the lead just seconds before Mata converted an even more difficult opportunity for Chelsea.

Cesar Azpilicueta also deserved considerable credit for his part in the goal, delivering an incisive through ball that exposed the gaping hole between Bacary Sagna and Per Mertesacker in the Arsenal defence.

Wenger was apoplectic, not so much at defending of his team, but a blatant mistake from referee Martin Atkinson in missing Ramires' late tackle on Francis Coquelin at the start of Chelsea's attack.

There was further controversy for Chelsea's second, but, once again, also some terrible Arsenal defending.

Mertesacker continued to find himself sucked, almost schoolboy style, towards the ball, with Mata exploiting Sagna's positional indiscipline to put Ramires clear on goal. Szczesny went to ground, with Ramires knocking the ball past the Arsenal goalkeeper and then just glancing his leg before going down.

It appeared that the only point of debate would be whether Atkinson should send off Szczesny as well as award the penalty, but subsequent replays suggested that Ramires had consciously moved his leg towards Szczesny just before contact.

Atkinson sided with Ramires in awarding a penalty, but, having made that decision, was generous in allowing Szczesny to escape with a booking.

For Benitez and Abramovich, an added bonus of all the controversy was that it should arrive in the 16th minute and distract Chelsea fans from their usual chant in appreciation of Roberto di Matteo.

Lampard, inevitably, converted the penalty and it seemed that the main interest for the rest of the afternoon would be whether Arsenal were humiliated or merely beaten.

Chelsea initially maintained their control, but, despite overrunning Arsenal in central midfield, they were repeatedly let down by Torres. And his lack of certainty, confidence and killer instinct gradually seemed to seep through the team.

Mertesacker and Theo Walcott had both tested Petr Cech shortly after the restart before Chelsea's lead was deservedly halved. Santi Cazorla, who had been virtually anonymous until that point, delivered a perfectly-timed pass after spotting Walcott lurking between Ashley Cole and Branislav Ivanovic.

Walcott's pace ensured a clear run at goal and, demonstrating the calmness in front of goal that has persuaded Wenger to make him the club's highest-paid player, he opened up his body and side-footed the ball past Cech.

Chelsea were now clinging on, with Benitez prompting the only real cheer from Chelsea fans during the second-half by finally replacing Torres with Demba Ba. His impact was immediate.

With Sagna and Szczesny again caught out of position, Ba sprinted clear on goal only to be denied by Thomas Vermaelen's goal-line heroics.